**IAS/Park City Mathematics Series**

Volume: 8;
2000;
340 pp;
Softcover

MSC: Primary 22;
Secondary 43; 57

Print ISBN: 978-1-4704-2314-8

Product Code: PCMS/8.S

List Price: $60.00

Individual Member Price: $48.00

**Electronic ISBN: 978-1-4704-3907-1
Product Code: PCMS/8.E**

List Price: $60.00

Individual Member Price: $48.00

# Representation Theory of Lie Groups

Share this page *Edited by *
*Jeffrey Adams; David Vogan*

A co-publication of the AMS and IAS/Park City Mathematics Institute

This book contains written versions of the lectures given at
the PCMI Graduate Summer School on the representation theory of Lie
groups. The volume begins with lectures by A. Knapp and P. Trapa
outlining the state of the subject around the year 1975, specifically,
the fundamental results of Harish-Chandra on the general structure of
infinite-dimensional representations and the Langlands
classification.

Additional contributions outline developments in four of the most
active areas of research over the past 20 years. The clearly written
articles present results to date, as follows: R. Zierau and
L. Barchini discuss the construction of representations on Dolbeault
cohomology spaces. D. Vogan describes the status of the
Kirillov-Kostant “philosophy of coadjoint orbits” for
unitary representations. K. Vilonen presents recent advances in the
Beilinson-Bernstein theory of “localization”. And Jian-Shu Li
covers Howe's theory of “dual reductive
pairs”.

Each contributor to the volume presents the topics in a unique,
comprehensive, and accessible manner geared toward advanced graduate
students and researchers. Students should have completed the standard
introductory graduate courses for full comprehension of the work. The
book would also serve well as a supplementary text for a course on
introductory infinite-dimensional representation theory.

Titles in this series are co-published with the Institute
for Advanced Study/Park City Mathematics Institute. Members of the
Mathematical Association of America (MAA) and the National Council of
Teachers of Mathematics (NCTM) receive a 20% discount from list
price. *NOTE: This discount does not apply to volumes in this
series co-published with the Society for Industrial and Applied
Mathematics (SIAM).*

#### Readership

Graduate students and research mathematicians interested in representation theory specifically Lie groups and their representations.

#### Reviews & Endorsements

Altogether, the volume brings a coherent description of an important and beautiful part of representation theory, which certainly will be of substantial use for postgraduate students and mathematicians interested in the area.

-- European Mathematical Society Newsletter

#### Table of Contents

# Table of Contents

## Representation Theory of Lie Groups

- Cover Cover11
- Title page v6
- Contents vii8
- Preface xi12
- Introduction 114
- Representations of semisimple Lie groups 518
- Representations in Dolbeault cohomology 89102
- Unitary representations attached to elliptic orbits. A geometric approach 147160
- The method of adjoint orbits for real reductive groups 177190
- Geometric methods in representation theory 239252
- Minimal representations and reductive dual pairs 291304
- Back Cover Back Cover1354